Got to be at least 40 cal whatever it is. Looking on line the 40-70 Sharps bottle neck looks close but not quite the same as what you have.
https://www.buffaloarms.com/40-70-sharps-bottle-neck-ammo-amobp4070sbnorig.html
Could be the Federal and Browning nickel plated cases just happen to be from good lots of brass. The nickel plated W-W 6.8 Western brass I have does seem to shoot better on average compared the standard brass also from Winchester. Maybe it's coincidence or maybe there's something to it, we'll...
Looks like they added a fancy wood stocked version of the model 307 for those who like that. Weatherby sure does know how to do a wood stock.
https://weatherby.com/store/model-307-adventure-sd/